Method for separating out a defect image from a thermogram sequence based on weighted naive bayesian classifier and dynamic multi-objective optimization

ABSTRACT

The present invention provides a method for separating out a defect image from a thermogram sequence based on weighted naive Bayesian classifier and dynamic multi-objective optimization, we find that different kinds of TTRs have big differences in some physical quantities. The present invention extracts these features (physical quantities) and classifies the selected TTRs into K categories based on their feature vectors through a weighted naive Bayesian classifier, which deeply digs the physical meanings contained in each TTR, makes the classification of TTRs more rational, and improves the accuracy of defect image&#39;s separation. Meanwhile, the multi-objective function does not only fully consider the similarities between the RTTR and other TTRs in the same category, but also considers the dissimilarities between the RTTR and the TTRs in other categories, thus the RTTR selected is more representative, which guarantees the accuracy of describing the defect outline. And the initial TTR population corresponding to the approximate solution for multi-objective optimization is chosen according to the previous TTR populations, which makes the multi-objective optimization dynamic and reduces its time consumption.

FIELD OF THE INVENTION

This application claims priorities under the Paris Convention to ChinesePatent Application No. 201810527601.6, filed May 29, 2018, ChinesePatent Application No. 201811451824.5, filed Nov. 30, 2018, and ChinesePatent Application No. 201910019827.X, filed Jan. 9, 2019, the entiretyof which is hereby incorporated by reference for all purposes as iffully set forth herein.

The present invention relates to the field of Non-destructive Testing(NDT), more particularly to a method for separating out a defect imagefrom a thermogram sequence based on weighted Naive Bayesian classifierand multi-objective optimization.

BACKGROUND OF THE INVENTION

Non-destructive Testing (NDT) is a wide group of analysis techniquesused in science and technology industry to evaluate the properties of amaterial, component or system without causing damage. Infrared thermalimage detection is one kind of NDT, which obtains the structureinformation of material through the control of heating and themeasurement of surface temperature variation.

Infrared thermal image detection is widely used in various fields ofnon-destructive testing, because it is fast, safe, and does not requiredirect contact. In the process of heating, the distribution of Jouleheat can be affected by the location of the defect(s) of the materialunder test. The high Joule heat leads to high temperature area and thelow Joule heat leads to low temperature area. The different temperaturescan be recorded by the infrared thermal imaging camera, then athermogram sequence is obtained. For a pixel in the thermogram sequence,its temperature variation with time is called as a transient thermalresponse (TTR). By distinguishing the difference of TTRs, we canseparate out a defect image from the thermal sequence.

In order to separate the defect image, many methods are used to processthe thermogram sequence, typical one of them is Fuzzy C-means (FCM). FCMclassifies the TTRS through clustering centers based on membershipvalues, its classification is a process of choosing a minimal distancebetween a TTR and each cluster center. Thus, FCM does not deeply dig thephysical meanings contained in each TTR, which makes the rationality ofclustering abated, and lowers the accuracy of defect separation.

SUMMARY OF THE INVENTION

The present invention aims to overcome the deficiencies of the prior artand provides a method for separating out a defect image from athermogram sequence based on weighted naive Bayesian classifier anddynamic multi-objective optimization so as to enhance the rationality ofclustering by deeply digging the physical meanings contained in eachTTR, thus the accuracy of defect separation is improved.

To achieve these objectives, in accordance with the present invention, amethod for separating out a defect image from a thermogram sequencebased on weighted naive Bayesian classifier and dynamic multi-objectiveoptimization is provided, comprising:

(1). taking a thermogram sequence, recorded by an infrared thermalimaging camera, as a three-dimensional (3D) matrix denoted by S, wherean element S(i,j,t) of 3D matrix S is a pixel value of row i and columnj of the thermogram sequence's frame t, each frame has I rows and Jcolumns;

(2). selecting G transient thermal responses (TTRs) from 3D matrix S,then extracting each TTR's features: E^(g), V_(up) ^(g), V_(down) ^(g),T_(ave) ^(g), T_(max) ^(g);

where E^(g) is the TTR's energy, and calculated according to thefollowing equation:E ^(g) =x _(g,1) ² +x _(g,2) ² + . . . +x _(g,T) ²

g is the serial number of the TTR, g=1, 2, . . . , G, x_(g,t) is thepixel value (temperature value) of TTR g at frame t, t represents 1, 2,. . . , T, T is the number of frames of the thermogram sequence;

where V_(up) ^(g) is the TTR's temperature change rate duringendothermic process, and calculated according to the following equation:

$V_{up}^{g} = \frac{x_{g,t_{mid}} - x_{g,t_{0}}}{t_{mid} - t_{0}}$

t_(mid) is the serial number of the last heating frame, x_(g,t) _(mid)is the pixel value (temperature value) of TTR g at frame t_(mid), t₀ isthe serial number of the first heating frame, x_(g,t) ₀ is the pixelvalue (temperature value) of TTR g at frame t₀;

where v_(down) ^(g) is the TTR's temperature change rate duringendothermic process, and calculated according to the following equation:

$V_{down}^{g} = \frac{x_{g,t_{mid}} - x_{g,t_{end}}}{t_{end} - t_{mid}}$

t_(end) is the serial number of the last heat releasing frame, x_(g,t)_(end) is the pixel value (temperature value) of TTR g at frame t_(end);

where T_(ave) ^(g) is the TTR's average temperature, and calculatedaccording to the following equation:

$T_{ave}^{g} = \frac{x_{g,1} + x_{g,2} + \ldots + x_{g,T}}{T}$

where T_(max) ^(g) is the TTR's maximum temperature, and calculatedaccording to the following equation:T _(max) ^(g)=max(x _(g,1) ,x _(g,2) , . . . ,x _(g,T));

(3). creating a feature vector for each TTR, where the feature vector isdenoted by X_(g)=(E^(g),V_(up) ^(g),V_(down) ^(g),T_(ave) ^(g),T_(max)^(g)), g=1, 2, . . . , G;

then discretizing the elements of feature vector X_(g), where thediscrete value of E^(g) is denoted by E₁, E₂, E₃ or E₄ according to thevalue of E^(g), the discrete value of V_(up) ^(g) is denoted by V_(up1),V_(up2), V_(up3) or V_(up4) according to the value of V_(up) ^(g), thediscrete value of V_(down) ^(g) is denoted by V_(down1), V_(down2),V_(down3) or V_(down4) according to the value of V_(down) ^(g), thediscrete value of T_(ave) ^(g) is denoted by T_(ave1), T_(ave2),T_(ave3) or T_(ave4) according to the value of T_(ave) ^(g), thediscrete value of T_(max) ^(g) is denoted by T_(max1), T_(max2),T_(max3) or T_(max4) according to the value of T_(max) ^(g);

then classifying the G TTRs into K′ categories based on their featurevectors through a weighted naive Bayesian classifier, where the weightednaive Bayesian classifier is:

${h_{nb}( X_{g} )} = {\arg\;{\max\limits_{c_{k} \in C}{{p( c_{k} )}{p( {X_{g}❘c_{k}} )}}}}$

c_(k) is the k^(th) category of the G TTRs, C is a class set and denotedby C=(c₁, c₂, . . . , c_(K′)), h_(nb)(X_(g)) is the category of theg^(th) TTR classified by its feature vector X_(g), i.e. category c_(k)which has the maximal value of p(c_(k))p(X_(g)|c_(k)) is the category ofthe g^(th) TTR;

where p(c_(k)) is the prior probability of category c_(k), and its valueis:

${p( c_{k} )} = \frac{N_{c_{k}}}{N_{total}}$

N_(total) is the number of historic TTRs used for training, N_(c) _(k)is the number of the TTRs which belong to category c_(k) among thehistoric TTRs;

where p(X_(g)|c_(k)) is the likelihood probability that the g^(th) TTRbelongs to category c_(k), and its value is:

p(X_(g)❘c_(k)) = p(E^(g)❘c_(k))^(w_(E)) ⋅ p(V_(up)^(g)❘c_(k))^(w_(V_(up))) ⋅ p(V_(down)^(g)❘c_(k))^(w_(V_(down))) ⋅ p(T_(ave)^(g)❘c_(k))^(w_(T_(ave))) ⋅ p(T_(max)^(g)❘c_(k))^(w_(T_(max)))

the weights w_(E), w_(V) _(up) , w_(V) _(down) , w_(T) _(ave) , w_(T)_(max) are.

$w_{E} = {\quad{{\frac{\begin{matrix}{{\frac{N_{E_{1}}}{N_{total}} \cdot {{KL}( C \middle| E_{1} )}} + {{\frac{N_{E_{2}}}{N_{total}} \cdot {KL}}( C \middle| E_{2} )} +} \\{{\frac{N_{E_{3}}}{N_{total}} \cdot {{KL}( C \middle| E_{3} )}} + {\frac{N_{E_{4}}}{N_{total}} \cdot {{KL}( C \middle| E_{4} )}}}\end{matrix}}{Z}w_{V_{up}}} = {\quad{{\frac{\begin{matrix}{{\frac{N_{V_{{up}\; 1}}}{N_{total}} \cdot {{KL}( C \middle| V_{{up}\; 1} )}} + {\frac{N_{V_{{up}\; 2}}}{N_{total}} \cdot {{KL}( C \middle| V_{{up}\; 2} )}} +} \\{{\frac{N_{V_{{up}\; 3}}}{N_{total}} \cdot {{KL}( C \middle| V_{{up}\; 3} )}} + {\frac{N_{V_{{up}\; 4}}}{N_{total}} \cdot {{KL}( C \middle| V_{{up}\; 4} )}}}\end{matrix}}{Z}w_{V_{down}}} = {\quad{{\frac{\begin{matrix}{{\frac{N_{V_{{down}\; 1}}}{N_{total}} \cdot {{KL}( C \middle| V_{{down}\; 1} )}} + {\frac{N_{V_{{down}\; 2}}}{N_{total}} \cdot {{KL}( C \middle| V_{{down}\; 2} )}} +} \\{{\frac{N_{V_{{down}\; 3}}}{N_{total}} \cdot {{KL}( C \middle| V_{{down}\; 3} )}} + {\frac{N_{V_{{down}\; 4}}}{N_{total}} \cdot {{KL}( C \middle| V_{{down}\; 4} )}}}\end{matrix}}{Z}w_{T_{ave}}} = {\quad{{\frac{\begin{matrix}{{\frac{N_{T_{{ave}\; 1}}}{N_{total}} \cdot {{KL}( C \middle| T_{{ave}\; 1} )}} + {\frac{N_{T_{{ave}\; 2}}}{N_{total}} \cdot {{KL}( C \middle| T_{{ave}\; 2} )}} +} \\{{\frac{N_{T_{{ave}\; 3}}}{N_{total}} \cdot {{KL}( C \middle| T_{{ave}\; 3} )}} + {\frac{N_{T_{{ave}\; 4}}}{N_{total}} \cdot {{KL}( C \middle| T_{{ave}\; 4} )}}}\end{matrix}}{Z}w_{T_{\max}}} = {\quad{{\frac{\begin{pmatrix}{{\frac{N_{T_{\max\; 1}}}{N_{total}} \cdot {{KL}( C \middle| T_{\max\; 1} )}} + {\frac{N_{T_{\max\; 2}}}{N_{total}} \cdot {{KL}( C \middle| T_{\max\; 2} )}} +} \\{{\frac{N_{T_{\max\; 3}}}{N_{total}} \cdot {{KL}( C \middle| T_{\max\; 3} )}} + {\frac{N_{T_{\max\; 4}}}{N_{total}} \cdot {{KL}( C \middle| T_{\max\; 4} )}}}\end{pmatrix}}{(Z)}{where}Z} = {\sum\limits_{h = 1}^{4}{\quad{{{\begin{pmatrix}\begin{matrix}{{N_{E_{h}}{{KL}( C \middle| E_{h} )}} + {N_{V_{uph}}{KL}( C \middle| V_{uph} )} +} \\{{N_{V_{downh}}{{KL}( C \middle| V_{downh} )}} +}\end{matrix} \\{{N_{T_{aveh}}{{KL}( C \middle| T_{aveh} )}} + {N_{T_{maxh}}{{KL}( C \middle| T_{maxh} )}}}\end{pmatrix}/5}N_{total}{where}{{KL}( C \middle| E_{h} )}} = {{\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| E_{h} )}{\log( \frac{p( c_{k} \middle| E_{h} )}{p( c_{k} )} )}{{KL}( C \middle| V_{uph} )}}} = {{\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| V_{uph} )}{\log( \frac{p( c_{k} \middle| V_{uph} )}{p( c_{k} )} )}{{KL}( C \middle| V_{downh} )}}} = {{\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| V_{downh} )}{\log( \frac{p( c_{k} \middle| V_{downh} )}{p( c_{k} )} )}{{KL}( C \middle| T_{aveh} )}}} = {{\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| T_{aveh} )}{\log( \frac{p( c_{k} \middle| T_{aveh} )}{p( c_{k} )} )}{{KL}( C \middle| T_{maxh} )}}} = {\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| T_{maxh} )}{\log( \frac{p( c_{k} \middle| T_{maxh} )}{p( c_{k} )} )}}}}}}}}}}}}}}}}}}}}$

where N_(E) ₁ , N_(E) ₂ , N_(E) ₃ and N_(E) ₄ are respectively thenumber of the TTRs of discrete value E₁, the number of the TTRs ofdiscrete value E₂, the number of the TTRs of discrete value E₃ and thenumber of the TTRs of discrete value E₄ among the historic TTRs; N_(V)_(up1) , N_(V) _(up2) , N_(V) _(up3) and N_(V) _(up4) are respectivelythe number of the TTRs of discrete value V_(up1), the number of the TTRsof discrete value V_(up2), the number of the TTRs of discrete valueV_(up3) and the number of the TTRs of discrete value V_(up4) among thehistoric TTRs; N_(V) _(down1) , N_(V) _(down2) , N_(V) _(down3) andN_(V) _(down4) are respectively the number of the TTRs of discrete valueV_(down1), the number of the TTRs of discrete value V_(down1), thenumber of the TTRs of discrete value V_(down3) and the number of theTTRs of discrete value V_(down4) among the historic TTRs; N_(T) _(ave1), N_(T) _(ave2) , N_(T) _(ave3) and N_(T) _(ave4) are respectively thenumber of the TTRs of discrete value T_(ave1), the number of the TTRs ofdiscrete value T_(ave2), the number of the TTRs of discrete valueT_(ave3) and the number of the TTRs of discrete value T_(ave4) among thehistoric TTRs; N_(T) _(max1) , N_(T) _(max2) , N_(T) _(max3) and N_(T)_(max4) are respectively the number of the TTRs of discrete valueT_(max1), the number of the TTRs of discrete value T_(max2), the numberof the TTRs of discrete value T_(max3) and the number of the TTRs ofdiscrete value T_(max4) among the historic TTRs;

where h is the serial number of discrete value, KL is Kullback-Leiblerdivergence operation, p(c_(k)|E_(h)), p(c_(k)|V_(uph)),p(c_(k)|V_(downh)), p(c_(k)|T_(aveh)) and p(c_(k)|T_(max h)) arerespectively the posterior probability that discrete value E_(h) belongsto category c_(k), the posterior probability that discrete value,V_(uph) belongs to category c_(k), the posterior probability thatdiscrete value V_(downh) belongs to category c_(k), the posteriorprobability that discrete value T_(aveh) belongs to category c_(k) anddiscrete value T_(max h) belongs to category c_(k);

then discarding the categories in which the number of TTRs is less thana threshold to obtain K categories;

(4). selecting a RTTR (Representative Transient Thermal Response) foreach category based on feature vector through dynamic multi-objectiveoptimization, where the multi-objective function is:minimizeF(_(i′) X)=(f ₁(_(i′) X), . . . ,f _(K)(_(i′) X))^(T)

_(i′)X is a feature vector of a TTR selected from category i′,_(i′)X=(_(i′)Ē, _(i′) V _(up), _(i′) V _(down)), _(i′)Ē is thenormalized energy value of the TTR, _(i′) V _(up) is the normalizedtemperature change rate of the TTR during endothermic process, _(i′) V_(down) is the normalized temperature change rate of the TTR duringendothermic process, the center of feature vectors of category i′ isdenoted by _(i′)X_(center)=(_(i′)Ē_(Center), _(i′) V _(up_Center), _(i′)V _(down_Center));

f₁(_(i′)X) is the Euclidean distance between feature vector _(i′)X andcenter _(i′)X_(center), and can be calculated according to the followingequation:

${f_{1}{\,( {}_{i^{\prime}}X )}} = {\min\sqrt{( {{\,_{i^{\prime}}\overset{\_}{E}} - {{}_{i\prime}^{}{E\_}_{}^{}}} )^{2} + ( {{{}_{i\prime}^{}{V\_}_{}^{}} - {{}_{i\prime}^{}{V\_}_{{up}\_{Center}}^{}}} )^{2} + ( {{{}_{i\prime}^{}{V\_}_{}^{}} - {{}_{i\prime}^{}{V\_}_{{down}\_{Center}}^{}}} )^{2}}}$

f_(k)(_(i′)X), k=2, 3, . . . , K are renumbered Euclidean distancesf_(i′j′)(_(i′)X) between feature vector _(i′)X and center_(j′)X_(center) of feature vectors of category j′, j≠i′,_(j′)X_(center)=(_(j′)Ē_(Center), _(j′) V _(up_Center), _(j′) V_(down_Center)) and can be calculated according to the followingequation:

${f_{\underset{j^{\prime} \neq i^{\prime}}{i^{\prime}j^{\prime}}}{\,( {}_{i^{\prime}}X )}} = {\min( {- \sqrt{\begin{matrix}{( {{\,_{i^{\prime}}\overset{\_}{E}} - {{}_{j\prime}^{}{E\_}_{}^{}}} )^{2} + ( {{{}_{i\prime}^{}{V\_}_{}^{}} - {{}_{j\prime}^{}{V\_}_{{up}\_{Center}}^{}}} )^{2} +} \\( {{{}_{i\prime}^{}{V\_}_{}^{}} - {{}_{j\prime}^{}{V\_}_{{down}\_{Center}}^{}}} )^{2}\end{matrix}}} )}$

where the initial TTR population corresponding to the approximatesolution for multi-objective optimization is chosen according to the twoTTR populations respectively corresponding to the two approximatesolutions of previous two defect image separations;

(5). putting the RTTRs of K categories by column to create a matrix Y,where a column is a RTTR, which contains T pixel values of the RTTR, thematrix Y is a matrix with size of T×K;

(6). linking the back column to the front column from the first columnfor each frame of 3D matrix S to obtain T columns of pixels, putting theT columns of pixels by frame order to create a two-dimensional imagematrix O with I×J rows and T columns, then performing linertransformation to matrix Y with two-dimensional image matrix O:R=Y⁻¹*O^(T) to obtain a two-dimensional image matrix R, where Y⁻¹ is thepseudo-inverse matrix of matrix Y with size of K×T, O^(T) is thetranspose matrix of two-dimensional image matrix O, two-dimensionalimage matrix R has K rows and I×J columns;

(7). dividing a row of two-dimensional image matrix R into I rows bycolumn size of J, and putting the I rows together by order to obtain atwo-dimensional image with size of I×J, where two-dimensional imagematrix R has K rows, thus K two-dimensional images are obtained,selecting a two-dimensional image which has maximal difference of pixelvalue between defect area and non-defect area from the K two-dimensionalimages;

(8). using Fuzzy C-Mean algorithm to cluster the selectedtwo-dimensional image: obtaining each pixel's cluster according topixel's maximal membership, then setting the pixel value of each clustercenter to all pixels of the cluster which the cluster center belongs to,where the selected two-dimensional image is turned into a separatedimage, and converting the separated image into a binary image, where thebinary image is the defect image separated from the thermogram sequence.

The objectives of the present invention are realized as follows:

In the present invention, i.e. a method for separating out a defectimage from a thermogram sequence based on weighted naive Bayesianclassifier and dynamic multi-objective optimization, we find thatdifferent kinds of TTRs have big differences in some physicalquantities, such as the energy, temperature change rate duringendothermic process, temperature change rate during endothermic process,average temperature, maximum temperature. The present invention extractsthese features (physical quantities) and classifies the selected TTRsinto K categories based on their feature vectors through a weightednaive Bayesian classifier, which deeply digs the physical meaningscontained in each TTR, makes the classification of TTRs more rational,and improves the accuracy of defect image's separation.

Meanwhile, the present invention creates a multi-objective function toselect a RTTR for each category based on dynamic multi-objectiveoptimization. The multi-objective function does not only fully considerthe similarities between the RTTR and other TTRs in the same category,but also considers the dissimilarities between the RTTR and the TTRs inother categories, thus the RTTR selected is more representative, whichguarantees the accuracy of describing the defect outline. And theinitial TTR population corresponding to the approximate solution formulti-objective optimization is chosen according to the previous TTRpopulations, which makes the multi-objective optimization dynamic andreduces its time consumption.

BRIEF DESCRIPTION OF THE DRAWING

The above and other objectives, features and advantages of the presentinvention will be more apparent from the following detailed descriptiontaken in conjunction with the accompanying drawings, in which:

FIG. 1 is a flow diagram of a method for separating out a defect imagefrom a thermogram sequence based on weighted naive Bayesian classifierand dynamic multi-objective optimization in accordance with the presentinvention;

FIG. 2 is a diagram of a 3D matrix in accordance with one embodiment ofpresent invention;

FIG. 3 is a diagram of a frame which has pixel valueS(i_(zz),j_(zz),t_(zz)) in accordance with one embodiment of presentinvention;

FIG. 4 is a diagram of a row that pixel value S(i_(zz),j_(zz),t_(zz)) isat in accordance with one embodiment of present invention;

FIG. 5 is a diagram of dividing a 3D matrix S into Q+1 column datablocks in accordance with one embodiment of present invention;

FIG. 6 is a diagram of step length of column data block in accordancewith one embodiment of present invention;

FIG. 7 is a diagram of dividing a 3D matrix S into (P+1)×(Q+1) datablocks in accordance with one embodiment of present invention;

FIG. 8 is a diagram of TTRs selected from a data block in accordancewith one embodiment of present invention;

FIG. 9 is a diagram of being clustered into 3 clusters in accordancewith one embodiment of present invention;

FIGS. 10 (a), 10 (b), and 10 (c) are diagrams of 3 RTTRs selected from 3categories respectively in accordance with one embodiment of presentinvention;

FIG. 11 is a diagram of a defect image separated from a thermogramsequence in accordance with one embodiment of present invention;

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Hereinafter, preferred embodiments of the present invention will bedescribed with reference to the accompanying drawings. It should benoted that the similar modules are designated by similar referencenumerals although they are illustrated in different drawings. Also, inthe following description, a detailed description of known functions andconfigurations incorporated herein will be omitted when it may obscurethe subject matter of the present invention.

Embodiment

FIG. 1 is a flow diagram of a method for separating out a defect imagefrom a thermogram sequence based on weighted naive Bayesian classifierand dynamic multi-objective optimization in accordance with the presentinvention.

In one embodiment, as shown in FIG. 1, the method for separating out adefect image from a thermogram sequence based on weighted naive Bayesianclassifier and dynamic multi-objective optimization is provided,comprising:

Step S1: taking a thermogram sequence, recorded by an infrared thermalimaging camera, as a three-dimensional (3D) matrix S, where an elementS(i,j,t) of the 3D matrix S is a pixel value of row i and column j ofthe thermogram sequence's frame t. As shown in FIG. 2, each frame has Irows and J columns, and the 3D matrix S has T frames.

Step S2: selecting G transient thermal responses (TTRs) from 3D matrixS, then extracting each TTR's features: E^(g), V_(up) ^(g), V_(down)^(g), T_(max) ^(g), T_(ave) ^(g);

where E^(g) is the TTR's energy, and calculated according to thefollowing equation:E ^(g) =x _(g,1) ² +x _(g,2) ² + . . . +x _(g,T) ²

g is the serial number of the TTR, g=1, 2, . . . , G, x_(g,t) is thepixel value (temperature value) of TTR g at frame t, t represents 1, 2,. . . , T, T is the number of frames of the thermogram sequence;

where V_(up) ^(g) is the TTR's temperature change rate duringendothermic process, and calculated according to the following equation:

$V_{up}^{g} = \frac{x_{g,t_{mid}} - x_{g,t_{0}}}{t_{mid} - t_{0}}$

t_(mid) is the serial number of the last heating frame, x_(g,t) _(mid)is the pixel value (temperature value) of TTR g at frame t_(mid), to isthe serial number of the first heating frame, x_(g,t) ₀ to is the pixelvalue (temperature value) of TTR g at frame t₀;

where v_(down) ^(g) is the TTR's temperature change rate duringendothermic process, and calculated according to the following equation:

$V_{down}^{g} = \frac{x_{g,t_{mid}} - x_{g,t_{end}}}{t_{end} - t_{mid}}$

t_(end) is the serial number of the last heat releasing frame, x_(g,t)_(end) is the pixel value (temperature value) of TTR g at frame t_(end);

where T_(ave) ^(g) is the TTR's average temperature, and calculatedaccording to the following equation:

$T_{ave}^{g} = \frac{x_{g,1} + x_{g,2} + \ldots + x_{g,T}}{T}$

where T_(max) ^(g) is the TTR's maximum temperature, and calculatedaccording to the following equation:T _(max) ^(g)=max(x _(g,1) ,x _(g,2) , . . . ,x _(g,T));

In one embodiment, the selecting G transient thermal responses (TTRs)from 3D matrix S further comprises:

Step S201: selecting a pixel value S(i_(zz),j_(zz),t_(zz)) from 3Dmatrix S, where the pixel value S(i_(zz),j_(zz),t_(zz)) is the maximalpixel value at row i_(zz) and column j_(zz) and satisfies the followingequation:

$\max( {{S( {i_{zz},j_{zz},t_{zz}} )}\frac{{S( {i_{zz},j_{zz},t_{mid}} )} - {S( {i_{zz},j_{zz},t_{0}} )}}{t_{mid} - t_{0}}} )$

t_(mid) is the serial number of the last heating frame, t₀ is the serialnumber of the first heating frame.

As shown in FIG. 2, the frame T_(zz) is taken out from the 3D matrix S.As shown in FIG. 3, the frame T_(zz) has the pixel valueS(i_(zz),j_(zz),t_(zz)) satisfied with the equation at row i_(zz) andcolumn j_(zz).

Step S202: selecting column j_(zz) of frame t_(zz) from 3D matrix S, andchoosing jumping points according to pixel value's variation of columnj_(zz) of frame t_(zz), where a jumping point is located between twoadjacent pixels which pixel value's difference is greater than athreshold, and the number of jumping points is P, there has P jumpingpoints, then dividing 3D matrix S into P+1 row data blocks by rows whichthe P jumping points belong to;

selecting the maximal pixel value S^(p)(i_(zz) ^(p),j_(zz) ^(p),t_(zz)^(p)) from the p^(th) row data block denoted by S^(p), p=1, 2, . . . ,P+1, where i_(zz) ^(p), j_(zz) ^(p), and t_(zz) ^(p) are respectivelythe row number, column number and frame number of the pixel which hasthe maximal pixel value, thus the TTR corresponding to the maximal pixelvalue S^(p)(i_(zz) ^(p),j_(zz) ^(p),t_(zz) ^(p)) is S^(p)(i_(zz)^(p),j_(zz) ^(p),t), t=1, 2, . . . , T;

setting the temperature threshold of p^(th) row data block to THRE^(p),then calculating the correlation Re^(b) between TTR S^(p)(i_(zz)^(p),j_(zz) ^(p),t) and TTR S^(p)(i_(zz) ^(p)±b,j_(zz) ^(p),t), wherepixel interval b is set to 1, 2, . . . , in order, meanwhile, judgingthe correlation Re^(b): when the correlation Re^(b) is smaller thanTHRE^(p), stopping the calculation of the correlation Re^(b), wherepixel interval b is the step length CL^(p) of the row data block S^(p);

Step S203: selecting row i_(zz) of frame t_(zz) from 3D matrix S, andchoosing jumping points according to pixel value's variation of rowi_(zz) of frame t_(zz), where a jumping point is located between twoadjacent pixels which pixel value's difference is greater than athreshold, and the number of jumping point is Q, there has Q jumpingpoints, then dividing 3D matrix S into Q+1 column data blocks by columnswhich the Q jumping points belong to;

selecting the maximal pixel value S^(q)(i_(zz) ^(q),j_(zz) ^(q),t_(zz)^(q)) from the q^(th) column data block S^(q), q=1, 2, . . . , Q+1,where i_(zz) ^(q), j_(zz) ^(q), and t_(zz) ^(q) are respectively the rownumber, column number and frame number of the pixel which has themaximal pixel value, thus the TTR corresponding to the maximal pixelvalue S^(q)(i_(zz) ^(q),j_(zz) ^(q),t_(zz) ^(q)) is S^(q)(i_(zz)^(q),j_(zz) ^(q),t_(zz) ^(q)), t=1, 2, . . . , T;

setting the temperature threshold of q^(th) row data block to THRE^(q),then calculating the correlation Re^(d) between TTR S^(q)(i_(zz)^(q),j_(zz) ^(q),t_(zz) ^(q)) and TTR S^(q)(i_(zz) ^(q),j_(zz)^(q)±d,t), where pixel interval d is set to 1, 2, . . . , in order,meanwhile, judging the correlation Re^(d): when the correlation Re^(d)is smaller than THRE^(d), stopping the calculation of the correlationRe^(d), where pixel interval d is the step length CL^(p) of the columndata block S^(q).

In the embodiment, the column data blocks is taken as a example. Asshown in FIG. 3, row i_(zz) of frame t_(zz) is taken out from the 3Dmatrix S. As shown in FIG. 4, Q jumping points are chosen according topixel value's variation of row i_(zz) of frame t_(zz), where a jumpingpoint is located between two adjacent pixels which pixel value'sdifference is greater than a threshold. As shown in FIG. 5, the 3Dmatrix S is divided into Q+1 column data blocks by columns which the Qjumping points belong to. As shown in FIG. 6, d is the step lengthCL^(p) of the q^(th) column data block S^(q), when the correlationRe^(d) is smaller than temperature threshold THRE^(d).

Step S204: dividing the 3D matrix S into (P+1)×(Q+1) data blocks by therows which the P jumping points belong to and by columns which the Qjumping points belong to, where the data block at p^(th) by row andq^(th) by column is S^(p,q). As shown in FIG. 7, (P+1)×(Q+1) data blocksis obtained;

Step S205: for each data block S^(p,q), setting a threshold DD andinitializing set number g=1 and pixel location i=1, j=1, then storingthe TTR S(i_(zz),j_(zz),t) t=1, 2, . . . , T in set X(g), calculatingthe correlation Re_(i,j) between set X(g) and the TTR S^(p,q)(i,j,t),t=1, 2, . . . , T at i^(th) row, j^(th) column, and judging: ifRe_(i,j)<DD, then g=g+1, and storing the TTR S^(p,q)(i,j,t), t=1, 2, . .. , T in set X(g), otherwise i=i+CL^(p), and continuing to calculate thecorrelation Re_(i,j) between set X(g) and the TTR S^(p,q)(i,j,t), t=1,2, . . . , T at i^(th) row, j^(th) column and judge, where if i>M^(p,q),then i=i−M^(p,q), j=j+CL^(q), if j>N^(p,q), then terminating thecalculation and judgment, each set X(g) is a selected TTR, M^(p,q),N^(p,q) are respectively the number of rows and the number of columns ofdata block S^(p,q). As shown in FIG. 8, the TTRs corresponding to theblack boxes are TTRs selected from the data block S^(p,q), which arejudged and selected by step length CL^(p), CL^(q).

putting selected TTRs of all data blocks together to obtain the Gtransient thermal responses, the selection of G transient thermalresponses (TTRs) from the 3D matrix S is finished. In one embodiment,240 TTRs is obtained.

Step S3: creating a feature vector for each TTR, where the featurevector is denoted by X_(g)=(E^(g),V_(up) ^(g),V_(down) ^(g),T_(ave)^(g),T_(max) ^(g)) g=1, 2, . . . , G, then discretizing the elements offeature vector X_(g), where the discrete value of E^(g) is denoted byE₁, E₂, E₃ or E₄ according to the value of E^(g), the discrete value ofV_(up) ^(g) is denoted by V_(up1), V_(up2), V_(up3) or V_(up4) accordingto the value of V_(up) ^(g), the discrete value of V_(down) ^(g) isdenoted by V_(down1), V_(down2), V_(down3) or V_(down4) according to thevalue of V_(down) ^(g), the discrete value of T_(ave) ^(g) is denoted byT_(ave1), T_(ave1), T_(ave3) or T_(ave4) according to the value ofT_(ave) ^(g), the discrete value of T_(max) ^(g) is denoted by T_(max1),T_(max2), T_(max3) or T_(max4) according to the value of T_(max) ^(g);

then classifying the G TTRs into K′ categories based on their featurevectors through a weighted naive Bayesian classifier, where the weightednaive Bayesian classifier is:

${h_{nb}( X_{g} )} = {\arg\underset{c_{k} \in C}{\;\max}\;{p( c_{k} )}{p( {X_{g}❘c_{k}} )}}$

c_(k) is the k^(th) category of the G TTRs, C is a class set and denotedby C=(c₁, c₂, . . . , c_(K′)), h_(nb)(X_(g)) is the category of theg^(th) TTR classified by its feature vector X_(g), i.e. category c_(k)which has the maximal value of p(c_(k))p(X_(g)|c_(k)) is the category ofthe g^(th) TTR;

where p(c_(k)) is the prior probability of category c_(k), and its valueis:

${p( c_{k} )} = \frac{N_{c_{k}}}{N_{total}}$

N_(total) is the number of historic TTRs used for training, N_(c) _(k)is the number of the TTRs which belong to category c_(k) among thehistoric TTRs;

where p(X_(g)|c_(k)) is the likelihood probability that the g^(th) TTRbelongs to category c_(k), and its value is:

p(X_(g)|c_(k)) = p(E^(g)|c_(k))^(w_(E)) ⋅ p(V_(up)^(g)|c_(k))^(w_(V_(up))) ⋅ p(V_(down)^(g)|c_(k))^(w_(V_(down))) ⋅ p(T_(ave)^(g)|c_(k))^(w_(T_(ave))) ⋅ p(T_(max)^(g)|c_(k))^(w_(T_(max)))

the weights w_(E), w_(V) _(up) , w_(V) _(down) , w_(T) _(ave) , w_(T)_(max) are:

$w_{E} = {\quad{{\frac{\begin{matrix}{{\frac{N_{E_{1}}}{N_{total}} \cdot {{KL}( C \middle| E_{1} )}} + {{\frac{N_{E_{2}}}{N_{total}} \cdot {KL}}( C \middle| E_{2} )} +} \\{{\frac{N_{E_{3}}}{N_{total}} \cdot {{KL}( C \middle| E_{3} )}} + {\frac{N_{E_{4}}}{N_{total}} \cdot {{KL}( C \middle| E_{4} )}}}\end{matrix}}{Z}w_{V_{up}}} = {\quad{{\frac{\begin{matrix}{{\frac{N_{V_{{up}\; 1}}}{N_{total}} \cdot {{KL}( C \middle| V_{{up}\; 1} )}} + {\frac{N_{V_{{up}\; 2}}}{N_{total}} \cdot {{KL}( C \middle| V_{{up}\; 2} )}} +} \\{{\frac{N_{V_{{up}\; 3}}}{N_{total}} \cdot {{KL}( C \middle| V_{{up}\; 3} )}} + {\frac{N_{V_{{up}\; 4}}}{N_{total}} \cdot {{KL}( C \middle| V_{{up}\; 4} )}}}\end{matrix}}{Z}w_{V_{down}}} = {\quad{{\frac{\begin{matrix}{{\frac{N_{V_{{down}\; 1}}}{N_{total}} \cdot {{KL}( C \middle| V_{{down}\; 1} )}} + {\frac{N_{V_{{down}\; 2}}}{N_{total}} \cdot {{KL}( C \middle| V_{{down}\; 2} )}} +} \\{{\frac{N_{V_{{down}\; 3}}}{N_{total}} \cdot {{KL}( C \middle| V_{{down}\; 3} )}} + {\frac{N_{V_{{down}\; 4}}}{N_{total}} \cdot {{KL}( C \middle| V_{{down}\; 4} )}}}\end{matrix}}{Z}w_{T_{ave}}} = {\quad{{\frac{\begin{matrix}{{\frac{N_{T_{{ave}\; 1}}}{N_{total}} \cdot {{KL}( C \middle| T_{{ave}\; 1} )}} + {\frac{N_{T_{{ave}\; 2}}}{N_{total}} \cdot {{KL}( C \middle| T_{{ave}\; 2} )}} +} \\{{\frac{N_{T_{{ave}\; 3}}}{N_{total}} \cdot {{KL}( C \middle| T_{{ave}\; 3} )}} + {\frac{N_{T_{{ave}\; 4}}}{N_{total}} \cdot {{KL}( C \middle| T_{{ave}\; 4} )}}}\end{matrix}}{Z}w_{T_{\max}}} = {\quad{{\frac{\begin{pmatrix}{{\frac{N_{T_{\max\; 1}}}{N_{total}} \cdot {{KL}( C \middle| T_{\max\; 1} )}} + {\frac{N_{T_{\max\; 2}}}{N_{total}} \cdot {{KL}( C \middle| T_{\max\; 2} )}} +} \\{{\frac{N_{T_{\max\; 3}}}{N_{total}} \cdot {{KL}( C \middle| T_{\max\; 3} )}} + {\frac{N_{T_{\max\; 4}}}{N_{total}} \cdot {{KL}( C \middle| T_{\max\; 4} )}}}\end{pmatrix}}{(Z)}{where}Z} = {\sum\limits_{h = 1}^{4}{\quad{{{\begin{pmatrix}\begin{matrix}{{N_{E_{h}}{{KL}( C \middle| E_{h} )}} + {N_{V_{uph}}{KL}( C \middle| V_{uph} )} +} \\{{N_{V_{downh}}{{KL}( C \middle| V_{downh} )}} +}\end{matrix} \\{{N_{T_{aveh}}{{KL}( C \middle| T_{aveh} )}} + {N_{T_{maxh}}{{KL}( C \middle| T_{maxh} )}}}\end{pmatrix}/5}N_{total}{where}{{KL}( C \middle| E_{h} )}} = {{\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| E_{h} )}{\log( \frac{p( c_{k} \middle| E_{h} )}{p( c_{k} )} )}{{KL}( C \middle| V_{uph} )}}} = {{\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| V_{uph} )}{\log( \frac{p( c_{k} \middle| V_{uph} )}{p( c_{k} )} )}{{KL}( C \middle| V_{downh} )}}} = {{\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| V_{downh} )}{\log( \frac{p( c_{k} \middle| V_{downh} )}{p( c_{k} )} )}{{KL}( C \middle| T_{aveh} )}}} = {{\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| T_{aveh} )}{\log( \frac{p( c_{k} \middle| T_{aveh} )}{p( c_{k} )} )}{{KL}( C \middle| T_{maxh} )}}} = {\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| T_{maxh} )}{\log( \frac{p( c_{k} \middle| T_{maxh} )}{p( c_{k} )} )}}}}}}}}}}}}}}}}}}}}$

where N_(E) ₁ , N_(E) ₂ , N_(E) ₃ and N_(E) ₄ are respectively thenumber of the TTRs of discrete value E₁, the number of the TTRs ofdiscrete value E₂, the number of the TTRs of discrete value E₃ and thenumber of the TTRs of discrete value E₄ among the historic TTRs; N_(V)_(up1) , N_(V) _(up2) , N_(V) _(up3) and N_(V) _(up4) are respectivelythe number of the TTRs of discrete value V_(up1), the number of the TTRsof discrete value V_(up2), the number of the TTRs of discrete valueV_(up3) and the number of the TTRs of discrete value V_(up4) among thehistoric TTRs; N_(V) _(down1) , N_(V) _(down2) , N_(V) _(down3) andN_(V) _(down4) are respectively the number of the TTRs of discrete valueV_(down1), the number of the TTRs of discrete value V_(down2), thenumber of the TTRs of discrete value V_(down3) and the number of theTTRs of discrete value V_(down4) among the historic TTRs; N_(T) _(ave1), N_(T) _(ave2) , N_(T) _(ave3) and N_(T) _(ave4) are respectively thenumber of the TTRs of discrete value T_(ave1), the number of the TTRs ofdiscrete value T_(ave1), the number of the TTRs of discrete valueT_(ave3) and the number of the TTRs of discrete value T_(ave4) among thehistoric TTRs; N_(T) _(max1) , N_(T) _(max2) , N_(T) _(max3) and N_(T)_(max4) are respectively the number of the TTRs of discrete valueT_(max1), the number of the TTRs of discrete value T_(max2), the numberof the TTRs of discrete value T_(max3) and the number of the TTRs ofdiscrete value T_(max4) among the historic TTRs; where h is the serialnumber of discrete value, KL is Kullback-Leibler divergence operation,p(c_(k)|E_(h)), p(c_(k)|V_(uph)), p(c_(k)|V_(downh)), p(c_(k)|T_(aveh))and p(c_(k)|T_(max h)) are respectively the posterior probability thatdiscrete value E_(h) belongs to category c_(k), the posteriorprobability that discrete value, V_(uph) belongs to category c_(k), theposterior probability that discrete value V_(downh) belongs to categoryc_(k), the posterior probability that discrete value T_(aveh) belongs tocategory c_(k) and discrete value T_(max h) belongs to category c_(k);

then discarding the categories in which the number of TTRs is less thana threshold to obtain K categories;

In one embodiment, the features of 240 TTRs is classified into 20categories, and after discarding, 3 categories are obtained, whichinclude a non-defect category and two different defect categories. Theresult is shown in FIG. 9, there are 83 TTRs in non-defect category 142TTRs in defect 1 category and 9 TTRs in defect 2 category.

Step S4: selecting a RTTR (Representative Transient Thermal Response)for each category based on feature vector through dynamicmulti-objective optimization, where the multi-objective function is:minimizeF(_(i′) X)=(f ₁(_(i′) X), . . . ,f _(K)(_(i′) X))^(T)

_(i′)X is a feature vector of a TTR selected from category i′,_(i′)X=(_(i′)Ē, _(i′) V _(up), _(i′) V _(down)), _(i′)Ē is thenormalized energy value of the TTR, _(i′) V _(up) is the normalizedtemperature change rate of the TTR during endothermic process, _(i′) V_(down) is the normalized temperature change rate of the TTR duringendothermic process, the center of feature vectors of category i′ isdenoted by _(i′)X_(center)=(_(i′)Ē_(Center), _(i′) V _(up_Center),_(i′)V_(down_Center));

f_(k)(_(i′)X) is the Euclidean distance between feature vector _(i′)Xand center _(i′)X_(center), and can be calculated according to thefollowing equation:

${f_{1}{\,( {}_{i^{\prime}}X )}} = {\min\sqrt{( {{\,_{i^{\prime}}\overset{\_}{E}} - {{}_{i\prime}^{}{E\_}_{}^{}}} )^{2} + ( {{{}_{i\prime}^{}{V\_}_{}^{}} - {{}_{i\prime}^{}{V\_}_{{up}\_{Center}}^{}}} )^{2} + ( {{{}_{i\prime}^{}{V\_}_{}^{}} - {{}_{i\prime}^{}{V\_}_{{down}\_{Center}}^{}}} )^{2}}}$

f_(k)(_(i′)X), k=2, 3, . . . , K are renumbered Euclidean distancesf_(i′j′)(_(i′)X) between feature vector _(i′)X and center_(i′)X_(center) of feature vectors of category j′, j′≠i′,_(j′)X_(center)=(_(j′)Ē_(Center), _(j′) V _(up_Center),_(j′)V_(down_Center) and can be calculated according to the followingequation:

${f_{\underset{j^{\prime} \neq i^{\prime}}{i^{\prime}j^{\prime}}}{\,( {}_{i^{\prime}}X )}} = {\min( {- \sqrt{\begin{matrix}{( {{\,_{i^{\prime}}\overset{\_}{E}} - {{}_{j\prime}^{}{E\_}_{}^{}}} )^{2} + ( {{{}_{i\prime}^{}{V\_}_{}^{}} - {{}_{j\prime}^{}{V\_}_{{up}\_{Center}}^{}}} )^{2} +} \\( {{{}_{i\prime}^{}{V\_}_{}^{}} - {{}_{j\prime}^{}{V\_}_{{down}\_{Center}}^{}}} )^{2}\end{matrix}}} )}$

In one embodiment, the initial TTR population corresponding to theapproximate solution for multi-objective optimization is chosenaccording to the two TTR populations respectively corresponding to thetwo approximate solutions of previous two defect image separations bythe following steps:

Step A: randomly selecting N_(E) feature vectors from TTR population set_(i′) ⁻¹PS to form a TTR set _(i′) ⁻¹PS′, which is denoted by _(i′)⁻¹PS′=(_(i′) ⁻¹X′¹, _(i′) ⁻¹X′², . . . , _(i′) ⁻¹X′^(N) ^(E) ), randomlyselecting N_(E) feature vectors from TTR population set _(i′) ⁻²PS toform a TTR set _(i′) ⁻²PS′, where −1 represents the last defect imageseparation, −2 represents the second-to-last defect image separation,the TTR population set _(i′) ⁻¹PS corresponds to the approximatesolutions of category i′ of the last defect image separation, the TTRpopulation set _(i′) ⁻²PS corresponds to the approximate solutions ofcategory i′ of the second-to-last defect image separation;

marking the feature vector in TTR population set _(i′) ⁻²PS′ which isclosest to the n′^(th) feature vector in TTR population set _(i′) ⁻¹PS′as _(i′) ⁻²X′^(n′), where TTR population set _(i′) ⁻²PS is denoted by_(i′) ⁻²PS′=(_(i′) ⁻²X′¹, _(i′) ⁻²X′², . . . , _(i′) ⁻²X′^(N) ^(E) );

then calculating the number W of typical individuals in TTR set _(i′)⁻¹PS′:W=┌W ₁+_(i′) ⁻¹δ×(W ₂ −W ₁)┐

where W₁ and W₂ are respectively the lower limit value and the upperlimit value of W, and W₁=K+1, W₂=3K, _(i′) ⁻¹δ is estimate ofenvironment change of last defect image separation and obtainedaccording to the following equations:

${\,_{i^{\prime}}^{- 1}\delta} = \frac{\sum\limits_{n^{\prime} = 1}^{N_{E}}\sqrt{\sum\limits_{k = 1}^{K}\lbrack {{f_{k}( {{}_{i\prime}^{- 1}{}_{\;}^{\prime\; n^{\prime}}} )} - {f_{k}( {{}_{i\prime}^{- 2}{}_{\;}^{\prime\; n^{\prime}}} )}} \rbrack^{2}}}{N_{E} \times K}$

f_(k)(_(i′) ⁻¹X′^(n′)) is a f_(k)(_(i′)X) into which feature vector_(i′) ⁻¹X′^(n′) as feature vector _(i′)X is plugged, f_(k)(_(i′)⁻²X′^(n′)) is a f_(k)(_(i′)X) into which feature vector _(i′) ⁻²X′^(n′)as feature vector _(i′)X is plugged;

Step B: creating a multi-directional prediction set _(i′) ⁻¹C, whichincludes two parts, where the first part is the center of all featurevectors in TTR population set _(i′) ⁻¹PS and can be denote by _(i′)⁻¹XC¹:

${{}_{i\prime}^{- 1}{}_{}^{}} = {\frac{1}{{}_{i\prime}^{- 1}{}_{}^{}}{\sum\limits_{n = 1}^{{}_{i\prime}^{- 1}{}_{}^{}}{{}_{i\prime}^{- 1}{}_{}^{}}}}$

_(i′) ⁻¹X^(n) is the n^(th) feature vector in TTR population set _(i′)⁻¹PS, _(i′) ⁻¹N_(PS) is the number of feature vectors in TTR populationset _(i′) ⁻¹PS;

the second part is K extreme solutions of Pareto optimal front, and canbe denote by:_(i′) ⁻¹ XC ², . . . ,_(i′) ⁻¹ XC ^(N) ^(C)

N_(C) is the number of feature vectors in multi-directional predictionset _(i′) ⁻¹C, N_(C)=K+1;

Step C: calculating the Euclidean distance _(i′) ⁻¹D^(nw)=∥_(i′)⁻¹X^(n)−_(i′) ⁻¹XC^(w)∥₂ of the n^(th) feature vector _(i′) ⁻¹X^(n),_(i′) ⁻¹X^(n), n=1, 2, . . . , _(i′) ⁻¹N_(PS) from each feature vector_(i′) ⁻¹XC^(w), w=1, 2, . . . , N_(C), and putting the n^(th) featurevector _(i′) ⁻¹X^(n) into a cluster set which is corresponding to thefeature vector having minimal distance in multi-directional predictionset _(i′) ⁻¹C, thus TTR population set _(i′) ⁻¹PS is clustered intoN_(C) cluster sets which is denoted by _(i′) ⁻¹Cluster[w], w=1, 2, . . ., N_(C);

Step D: If N_(C)=W, outputting multi-directional prediction set _(i′)⁻¹C and the N_(C) cluster sets; otherwise adding a feature vector _(i′)⁻¹XC^(N) ^(C) ⁺¹ to multi-directional prediction set _(i′) ⁻¹C, thenupdating N_(C) with N_(C)=N_(C)+1 and returning to Step C, where featurevector _(i′) ⁻¹XC^(N) ^(ps) ⁺¹ is obtained through the followingequation:

${{}_{i\prime}^{- 1}{}_{}^{N_{ps} + 1}} = {\arg\limits_{\,_{i^{\prime}}^{- 1}X}{\max\limits_{w}{\max\limits_{l}{{{{}_{i\prime}^{- 1}{}_{}^{wl}} - {{}_{i\prime}^{- 1}{}_{}^{}}}}}}}$

_(i′) ⁻¹X^(w) _(l) is the l^(th) feature vector of _(i′) ⁻¹Cluster[w],i.e. feature vector _(i′) ⁻¹XC^(N) ^(C) ⁺¹ is a feature vector selectedfrom the N_(C) cluster sets which distance from its cluster center ismaximal;

Step E: calculating a prediction direction Δ_(i′) ⁻¹C={Δ_(i′) ⁻¹c¹,Δ_(i′) ⁻¹c², . . . , Δ_(i′) ⁻¹c^(W)}:Δ_(i′) ⁻¹ c ^(w)=_(i′) ⁻¹ XC ^(w)−_(i′) ⁻² XC ^(w′) ,w=1,2, . . . ,W

where _(i′) ⁻²XC^(w′) is a feature vector in multi-directionalprediction set _(i′) ⁻²C of the second-to-last defect image separationwhich is closest to feature vector _(i′) ⁻¹XC^(w);

Step F: initializing the size of the initial TTR populationcorresponding to the approximate solution to N_(p), where N_(p) isgreater than N_(E);

then creating N_(E) feature vectors, where the n^(th) feature vector ofthe N_(E) feature vectors is:_(i′) X ^(n′)(0)=_(i′) ⁻¹ X′ ^(n′)+Δ_(i′) ⁻¹ c ^(w) ^(n′) +_(i′) ⁻¹ε^(w)^(n′) ,n=1,2, . . . ,N _(E)

0 represents initial value of iteration of the dynamic multi-objectiveoptimization, w_(n′) is the serial number of the cluster set to whichfeature vector _(i′) ⁻¹X′^(n′) belongs, →_(i′) ⁻¹c^(w) ^(n′) is thew_(n′) ^(th) element in the prediction direction Δ_(i′) ⁻¹C, _(i′)⁻¹ε^(w) ^(n′) is a random number which obeys a normal distribution, themean of the normal distribution is 0, the variance of the normaldistribution is:

${\,_{i^{\prime}}^{- 1}\sigma} = {\frac{1}{W}{\sum\limits_{w = 1}^{W}{{\Delta_{i^{\prime}}^{- 1}c^{w}}}}}$

randomly creating N_(P)−N_(E) feature vectors;

combining the N_(E) feature vectors and the N_(P)−N_(E) feature vectorsto form the initial TTR population corresponding to the approximatesolution for multi-objective optimization.

In the embodiment, the previous TTR population provides a direction forthe creation of the initial TTR population corresponding to theapproximate solution, which makes the multi-objective optimizationdynamic and reduces its time consumption.

In one embodiment, as shown in FIG. 10, (a) is the RTTR of non-defectcluster, (b) is the RTTR of defect 1 cluster, (c) is the RTTR of defect2 cluster.

Step S5: putting the RTTRs of K categories by column to create a matrixY, where a column is a RTTR, which contains T pixel values of the RTTR,the matrix Y is a matrix with size of T×K;

Step S6: linking the back column to the front column from the firstcolumn for each frame of 3D matrix S to obtain T columns of pixels,putting the T columns of pixels by frame order to create atwo-dimensional image matrix O with I×J rows and T columns, thenperforming liner transformation to matrix Y with two-dimensional imagematrix O: R=Y⁻¹*O^(T) to obtain a two-dimensional image matrix R, whereY⁻¹ is the pseudo-inverse matrix of matrix Y with size of K×T, O^(T) isthe transpose matrix of two-dimensional image matrix O, two-dimensionalimage matrix R has K rows and I×J columns;

Step S7: dividing a row of two-dimensional image matrix R into I rows bycolumn size of J, and putting the I rows together by order to obtain atwo-dimensional image with size of I×J, where two-dimensional imagematrix R has K rows, thus K two-dimensional images are obtained,selecting a two-dimensional image which has maximal difference of pixelvalue between defect area and non-defect area from the K two-dimensionalimages;

Step S8: using Fuzzy C-Mean algorithm to cluster the selectedtwo-dimensional image: obtaining each pixel's cluster according topixel's maximal membership, then setting the pixel value of each clustercenter to all pixels of the cluster which the cluster center belongs to,where the selected two-dimensional image is turned into a separatedimage, and converting the separated image into a binary image, where thebinary image is the defect image separated from the thermogram sequence.

In one embodiment, as shown in FIG. 11, a defect image is separated froma thermogram sequence, there has two kind of defect, i.e. defect 1 anddefect 2.

While illustrative embodiments of the invention have been describedabove, it is, of course, understand that various modifications will beapparent to those of ordinary skill in the art. Such modifications arewithin the spirit and scope of the invention, which is limited anddefined only by the appended claims.

What is claimed is:
 1. A method for separating out a defect image from athermogram sequence based on weighted naive Bayesian classifier anddynamic multi-objective optimization, comprising: (1): taking athermogram sequence, recorded by an infrared thermal imaging camera, asa three-dimensional (3D) matrix denoted by S, where an element S(i,j,t)of 3D matrix S is a pixel value of row i and column j of the thermogramsequence's frame t, each frame has I rows and J columns; (2): selectingG transient thermal responses (TTRs) from 3D matrix S, then extractingeach TTR's features: E^(g), V_(up) ^(g), V_(down) ^(g), T_(ave) ^(g),T_(max) ^(g); where E^(g) is the TTR's energy, and calculated accordingto the following equation:E ^(g) =x _(g,1) ² +x _(g,2) ² + . . . +x _(g,T) ² g is the serialnumber of the TTR, g=1, 2, . . . , G, x_(g,t) is the pixel value(temperature value) of TTR g at frame t, t represents 1, 2, . . . , T, Tis the number of frames of the thermogram sequence; where v_(up) ^(g) isthe TTR's temperature change rate during endothermic process, andcalculated according to the following equation:$V_{up}^{g} = \frac{x_{g,t_{mid}} - x_{g,t_{0}}}{t_{mid} - t_{0}}$t_(mid) is the serial number of the last heating frame, x_(g,t) _(mid)is the pixel value (temperature value) of TTR g at frame t_(mid), t₀ isthe serial number of the first heating frame, x_(g,t) ₀ to is the pixelvalue (temperature value) of TTR g at frame t₀; where v_(down) ^(g) isthe TTR's temperature change rate during endothermic process, andcalculated according to the following equation:$V_{down}^{g} = \frac{x_{g,t_{mid}} - x_{g,t_{end}}}{t_{end} - t_{mid}}$t_(end) is the serial number of the last heat releasing frame, x_(g,t)_(end) to d is the pixel value (temperature value) of TTR g at framet_(end), where T_(ave) ^(g) is the TTR's average temperature, andcalculated according to the following equation:$T_{ave}^{g} = \frac{x_{g,1} + x_{g,2} + \ldots + x_{g,T}}{T}$ whereT_(max) ^(g) is the TTR's maximum temperature, and calculated accordingto the following equation:T _(max) ^(g)=max(x _(g,1) ,x _(g,2) , . . . ,x _(g,T)); (3): creating afeature vector for each TTR, where the feature vector is denoted byX_(g)=(E^(g),V_(up) ^(g),V_(down) ^(g),T_(ave) ^(g),T_(max) ^(g)), g=1,2, . . . , G; then discretizing the elements of feature vector X_(g),where the discrete value of E^(g) is denoted by E₁, E₂, E₃ or E₄according to the value of E^(g), the discrete value of V_(up) ^(g) isdenoted by V_(up1), V_(up2), V_(up3) or V_(up4) according to the valueof V_(up) ^(g), the discrete value of V_(down) ^(g) is denoted byV_(down1), V_(down2), V_(down3) or V_(down4) according to the value ofV_(ave) ^(g), the discrete value of T_(ave) ^(g) is denoted by T_(ave1),T_(ave2), T_(ave3) or T_(ave4) according to the value of T_(ave) ^(g),the discrete value of T_(max) ^(g) is denoted by T_(max1), T_(max2),T_(max3) or T_(max4) according to the value of T_(max) ^(g); thenclassifying the G TTRs into K′ categories based on their feature vectorsthrough a weighted naive Bayesian classifier, where the weighted naiveBayesian classifier is:${h_{nb}( X_{g} )} = {\arg\;{\max\limits_{c_{k} \in C}{{p( c_{k} )}{p( X_{g} \middle| c_{k} )}}}}$c_(k) is the k^(th) category of the G TTRs, C is a class set and denotedby C=(c₁, c₂, . . . , c_(K′)), h_(nb)(X_(g)) is the category of theg^(th) TTR classified by its feature vector X_(g), category c_(k) whichhas the maximal value of p(c_(k))p(X_(g)|c_(k)) is the category of theg^(th) TTR; where p(c_(k)) is the prior probability of category c_(k),and its value is:${p( c_{k} )} = \frac{N_{c_{k}}}{N_{total}}$ N_(total) is thenumber of historic TTRs used for training, N_(c) _(k) is the number ofthe TTRs which belong to category c_(k) among the historic TTRs; wherep(X_(g)|c_(k)) is the likelihood probability that the g^(th) TTR belongsto category c_(k), and its value is:p(X_(g)|c_(k)) = p(E^(g)|c_(k))^(w_(E)) ⋅ p(V_(up)^(g)|c_(k))^(w_(V_(up))) ⋅ p(V_(down)^(g)|c_(k))^(w_(V_(down))) ⋅ p(T_(ave)^(g)|c_(k))^(w_(T_(ave))) ⋅ p(T_(max)^(g)|c_(k))^(w_(T_(max)))the weights w_(E), w_(V) _(up) , w_(V) _(down) , w_(T) _(ave) , w_(T)_(max) are: $w_{E} = {\quad{{\frac{\begin{matrix}{{\frac{N_{E_{1}}}{N_{total}} \cdot {{KL}( C \middle| E_{1} )}} + {{\frac{N_{E_{2}}}{N_{total}} \cdot {KL}}( C \middle| E_{2} )} +} \\{{\frac{N_{E_{3}}}{N_{total}} \cdot {{KL}( C \middle| E_{3} )}} + {\frac{N_{E_{4}}}{N_{total}} \cdot {{KL}( C \middle| E_{4} )}}}\end{matrix}}{Z}w_{V_{up}}} = {\quad{{\frac{\begin{matrix}{{\frac{N_{V_{{up}\; 1}}}{N_{total}} \cdot {{KL}( C \middle| V_{{up}\; 1} )}} + {\frac{N_{V_{{up}\; 2}}}{N_{total}} \cdot {{KL}( C \middle| V_{{up}\; 2} )}} +} \\{{\frac{N_{V_{{up}\; 3}}}{N_{total}} \cdot {{KL}( C \middle| V_{{up}\; 3} )}} + {\frac{N_{V_{{up}\; 4}}}{N_{total}} \cdot {{KL}( C \middle| V_{{up}\; 4} )}}}\end{matrix}}{Z}w_{V_{down}}} = {\quad{{\frac{\begin{matrix}{{\frac{N_{V_{{down}\; 1}}}{N_{total}} \cdot {{KL}( C \middle| V_{{down}\; 1} )}} + {\frac{N_{V_{{down}\; 2}}}{N_{total}} \cdot {{KL}( C \middle| V_{{down}\; 2} )}} +} \\{{\frac{N_{V_{{down}\; 3}}}{N_{total}} \cdot {{KL}( C \middle| V_{{down}\; 3} )}} + {\frac{N_{V_{{down}\; 4}}}{N_{total}} \cdot {{KL}( C \middle| V_{{down}\; 4} )}}}\end{matrix}}{Z}w_{T_{ave}}} = {\quad{{\frac{\begin{matrix}{{\frac{N_{T_{{ave}\; 1}}}{N_{total}} \cdot {{KL}( C \middle| T_{{ave}\; 1} )}} + {\frac{N_{T_{{ave}\; 2}}}{N_{total}} \cdot {{KL}( C \middle| T_{{ave}\; 2} )}} +} \\{{\frac{N_{T_{{ave}\; 3}}}{N_{total}} \cdot {{KL}( C \middle| T_{{ave}\; 3} )}} + {\frac{N_{T_{{ave}\; 4}}}{N_{total}} \cdot {{KL}( C \middle| T_{{ave}\; 4} )}}}\end{matrix}}{Z}w_{T_{\max}}} = {\quad{{\frac{\begin{pmatrix}{{\frac{N_{T_{\max\; 1}}}{N_{total}} \cdot {{KL}( C \middle| T_{\max\; 1} )}} + {\frac{N_{T_{\max\; 2}}}{N_{total}} \cdot {{KL}( C \middle| T_{\max\; 2} )}} +} \\{{\frac{N_{T_{\max\; 3}}}{N_{total}} \cdot {{KL}( C \middle| T_{\max\; 3} )}} + {\frac{N_{T_{\max\; 4}}}{N_{total}} \cdot {{KL}( C \middle| T_{\max\; 4} )}}}\end{pmatrix}}{(Z)}{where}Z} = {\sum\limits_{h = 1}^{4}{\quad{{{\begin{pmatrix}\begin{matrix}{{N_{E_{h}}{{KL}( C \middle| E_{h} )}} + {N_{V_{uph}}{KL}( C \middle| V_{uph} )} +} \\{{N_{V_{downh}}{{KL}( C \middle| V_{downh} )}} +}\end{matrix} \\{{N_{T_{aveh}}{{KL}( C \middle| T_{aveh} )}} + {N_{T_{maxh}}{{KL}( C \middle| T_{maxh} )}}}\end{pmatrix}/5}N_{total}{where}{{KL}( C \middle| E_{h} )}} = {{\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| E_{h} )}{\log( \frac{p( c_{k} \middle| E_{h} )}{p( c_{k} )} )}{{KL}( C \middle| V_{uph} )}}} = {{\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| V_{uph} )}{\log( \frac{p( c_{k} \middle| V_{uph} )}{p( c_{k} )} )}{{KL}( C \middle| V_{downh} )}}} = {{\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| V_{downh} )}{\log( \frac{p( c_{k} \middle| V_{downh} )}{p( c_{k} )} )}{{KL}( C \middle| T_{aveh} )}}} = {{\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| T_{aveh} )}{\log( \frac{p( c_{k} \middle| T_{aveh} )}{p( c_{k} )} )}{{KL}( C \middle| T_{maxh} )}}} = {\sum\limits_{k = 1}^{K}{{p( c_{k} \middle| T_{maxh} )}{\log( \frac{p( c_{k} \middle| T_{maxh} )}{p( c_{k} )} )}}}}}}}}}}}}}}}}}}}}$where N_(E) ₁ , N_(E) ₂ , N_(E) ₃ and N_(E) ₄ are respectively thenumber of the TTRs of discrete value E₁, the number of the TTRs ofdiscrete value E₂, the number of the TTRs of discrete value E₃ and thenumber of the TTRs of discrete value E₄ among the historic TTRs; N_(V)_(up1) , N_(V) _(up2) , N_(V) _(up3) and N_(V) _(up4) are respectivelythe number of the TTRs of discrete value V_(up1), the number of the TTRsof discrete value V_(up2), the number of the TTRs of discrete valueV_(up3) and the number of the TTRs of discrete value V_(up4) among thehistoric TTRs; N_(V) _(down1) , N_(V) _(down2) , N_(V) _(down3) andN_(V) _(down4) are respectively the number of the TTRs of discrete valueV_(down1), the number of the TTRs of discrete value V_(down2), thenumber of the TTRs of discrete value V_(down3) and the number of theTTRs of discrete value V_(down4) among the historic TTRs; N_(T) _(ave1), N_(T) _(ave2) , _(T) _(ave3) and _(T) _(ave4) are respectively thenumber of the TTRs of discrete value T_(ave1), the number of the TTRs ofdiscrete value T_(ave2), the number of the TTRs of discrete valueT_(ave3) and the number of the TTRs of discrete value T_(ave4) among thehistoric TTRs; N_(T) _(max1) , N_(T) _(max2) , N_(T) _(max3) and N_(T)_(max4) are respectively the number of the TTRs of discrete valueT_(max1), the number of the TTRs of discrete value T_(max2), the numberof the TTRs of discrete value T_(max3) and the number of the TTRs ofdiscrete value T_(max4) among the historic TTRs; where h is the serialnumber of discrete value, KL is Kullback-Leibler divergence operation,p(c_(k)|E_(h)), p(c_(k)|V_(uph)), p(c_(k)|V_(downh)), p(c_(k)|T_(aveh))and p(c_(k)|T_(max h)) are respectively the posterior probability thatdiscrete value E_(h) belongs to category c_(k), the posteriorprobability that discrete value, V_(uph) belongs to category c_(k), theposterior probability that discrete value V_(downh) belongs to categoryc_(k), the posterior probability that discrete value T_(aveh) belongs tocategory c_(k) and discrete value T_(max h) belongs to category c_(k);then discarding the categories in which the number of TTRs is less thana threshold to obtain K categories; (4): selecting a RTTR(Representative Transient Thermal Response) for each category based onfeature vector through dynamic multi-objective optimization, where themulti-objective function is:minimizeF(_(i′) X)=(f ₁(_(i′) X), . . . ,f _(K)(_(i′) X))^(T) _(i′)X isa feature vector of a TTR selected from category i′,_(i′)X=(_(i′)Ē,_(i′) V _(up),_(i′) V _(down)), _(i′)Ē is the normalizedenergy value of the TTR, _(i′) V _(up) is the normalized temperaturechange rate of the TTR during endothermic process, _(i′) V _(down) isthe normalized temperature change rate of the TTR during endothermicprocess, the center of feature vectors of category i′ is denoted by_(i′)X_(center)=(_(i′)Ē_(Center),_(i′) V _(up_Center),_(i′) V_(down_Center)); f₁(_(i′)X) is the Euclidean distance between featurevector _(i′)X and center _(i′)X_(center), and can be calculatedaccording to the following equation:${f_{1}( {\,_{i^{\prime}}X} )} = {\min\sqrt{( {{\,_{i^{\prime}}\overset{\_}{E}} - {{}_{i\prime}^{}{E\_}_{}^{}}} )^{2} + ( {{{}_{i\prime}^{}{V\_}_{}^{}} - {{}_{i\prime}^{}{V\_}_{}^{}}} )^{2} + ( {{{}_{i\prime}^{}{V\_}_{}^{}} - {{}_{i\prime}^{}{V\_}_{}^{}}} )^{2}}}$f_(k)(_(i′)X), k=2, 3, . . . , K are renumbered Euclidean distancesf_(i′j′)(_(i′)X) between feature vector _(i′)X and center_(j′)X_(center) of feature vectors of category j′, j≠i′,_(j′)X_(center)=(_(j′)Ē_(Center),_(j′) V _(up_Center),_(j′) V_(down_Center)) and can be calculated according to the followingequation:${f_{\underset{j^{\prime} \neq i^{\prime}}{i^{\prime}j^{\prime}}}( {\,_{i^{\prime}}X} )} = {\min( {- \sqrt{\begin{matrix}{( {{\,_{i^{\prime}}\overset{\_}{E}} - {{}_{j\prime}^{}{E\_}_{}^{}}} )^{2} + ( {{{}_{i\prime}^{}{V\_}_{}^{}} - {{}_{j\prime}^{}{V\_}_{}^{}}} )^{2} +} \\( {{{}_{i\prime}^{}{V\_}_{}^{}} - {{}_{j\prime}^{}{V\_}_{}^{}}} )^{2}\end{matrix}}} )}$ where the initial TTR population correspondingto the approximate solution for multi-objective optimization is chosenaccording to the two TTR populations respectively corresponding to thetwo approximate solutions of previous two defect image separations; (5):putting the RTTRs of K categories by column to create a matrix Y, wherea column is a RTTR, which contains T pixel values of the RTTR, thematrix Y is a matrix with size of T×K; (6): linking the back column tothe front column from the first column for each frame of 3D matrix S toobtain T columns of pixels, putting the T columns of pixels together byframe order to create a two-dimensional image matrix O with I×J rows andT columns, then performing linear transformation to matrix Y withtwo-dimensional image matrix O: R−=Y⁻¹*O^(T) to obtain a two-dimensionalimage matrix R, where Y⁻¹ is the pseudo-inverse matrix of matrix Y withsize of K×T, O^(T) is the transpose matrix of two-dimensional imagematrix O, two-dimensional image matrix R has K rows and I×J columns;(7): dividing a row of two-dimensional image matrix R into I rows bycolumn size of J, and putting the I rows together by order to obtain atwo-dimensional image with size of I×J, where two-dimensional imagematrix R has K rows, thus K two-dimensional images are obtained,selecting a two-dimensional image which has maximal difference of pixelvalue between defect area and non-defect area from the K two-dimensionalimages; (8): using Fuzzy C-Mean algorithm to cluster the selectedtwo-dimensional image: obtaining each pixel's cluster according to thepixel's maximal membership, then setting the pixel value of each clustercenter to all pixels of the cluster which the cluster center belongs to,where the selected two-dimensional image is turned into a separatedimage, and converting the separated image into a binary image, where thebinary image is the defect image separated from the thermogram sequence.2. The method for separating out a defect image from a thermogramsequence based on weighted naive Bayesian classifier and dynamicmulti-objective optimization of claim 1, wherein the selecting Gtransient thermal responses (TTRs) from 3D matrix S comprises: selectinga pixel value S(i_(zz),j_(zz),t_(zz)) from 3D matrix S, where the pixelvalue S(i_(zz),j_(zz),t_(zz)) is the maximal pixel value at row i_(zz)and column j_(zz) and satisfies the following equation:$\max( {{S( {i_{zz},j_{zz},t_{zz}} )}\frac{{S( {i_{zz},j_{zz},t_{mid}} )} - {S( {i_{zz},j_{zz},t_{0}} )}}{t_{mid} - t_{0}}} )$t_(mid) is the serial number of the last heating frame, t₀ is the serialnumber of the first heating frame; selecting column j_(zz) of framet_(zz) from 3D matrix S, and choosing jumping points according to pixelvalue's variation of column j_(zz) of frame t_(zz), where a jumpingpoint is located between two adjacent pixels which pixel value'sdifference is greater than a threshold, and the number of jumping pointsis P, then dividing 3D matrix S into P+1 row data blocks by rows whichthe P jumping points belong to; selecting the maximal pixel valueS^(p)(i_(zz) ^(p),j_(zz) ^(p),t_(zz) ^(p)) from the p^(th) row datablock denoted by S^(p), p=1, 2, . . . , P+1, where i_(zz) ^(p), j_(zz)^(p), and t_(zz) ^(p) are respectively the row number, column number andframe number of the pixel which has the maximal pixel value, thus theTTR corresponding to the maximal pixel value S^(p)(i_(zz) ^(p),j_(zz)^(p),t_(zz) ^(p)) is S^(p)(i_(zz) ^(p),j_(zz) ^(p),t_(zz) ^(p)), t=1, 2,. . . , T; setting the temperature threshold of p^(th) row data block toTHRE^(p), then calculating the correlation Re^(b) between TTRS^(p)(i_(zz) ^(p),j_(zz) ^(p),t) and TTR S^(p)(i_(zz) ^(p)±b,j_(zz)^(p),t), where pixel interval b is set to 1, 2, . . . , in order,meanwhile, judging the correlation Re^(b): when the correlation Re^(b)is smaller than THRE^(p), stopping the calculation of the correlationRe^(b), where pixel interval b is the step length CL^(p) of the row datablock S^(p); selecting row i_(zz) of frame t_(zz) from 3D matrix S, andchoosing jumping points according to pixel value's variation of rowi_(zz) of frame t_(zz), where a jumping point is located between twoadjacent pixels which pixel value's difference is greater than athreshold, and the number of jumping point is Q, then dividing 3D matrixS into Q+1 column data blocks by columns which the Q jumping pointsbelong to; electing the maximal pixel value S^(q)(i_(zz) ^(q),j_(zz)^(q),t_(zz) ^(q)) from the q^(th) column data block S^(q), q=1, 2, . . ., Q+1, where i_(zz) ^(q), j_(zz) ^(q), and t_(zz) ^(q) are respectivelythe row number, column number and frame number of the pixel which hasthe maximal pixel value, thus the TTR corresponding to the maximal pixelvalue S^(q)(i_(zz) ^(q),j_(zz) ^(q),t_(zz) ^(q)) is S^(q)(i_(zz)^(q),j_(zz) ^(q),t), t=1, 2, . . . , T; setting the temperaturethreshold of q^(th) row data block to THRE^(q), then calculating thecorrelation Re^(d) between TTR S^(q)(i_(zz) ^(q),j_(zz) ^(q),t) and TTRS^(q)(i_(zz) ^(q),j_(zz) ^(q)±d,t), where pixel interval d is set to 1,2, . . . , in order, meanwhile, judging the correlation Re^(d): when thecorrelation Re^(d) is smaller than THRE^(d), stopping the calculation ofthe correlation Re^(d), where pixel interval d is the step length CL^(q)of the column data block S^(q); dividing the 3D matrix S into(P+1)×(Q+1) data blocks by the rows which the P jumping points belong toand by columns which the Q jumping points belong to, where the datablock at p^(th) by row and q^(th) by column is S^(p,q); for each datablock S^(p,q), setting a threshold DD and initializing set number g=1and pixel location i=1, j=1, then storing the TTR S(i_(zz),j_(zz),t),t=1, 2, . . . , T in set X(g), calculating the correlation Re_(i,j)between set X(g) and the TTR S^(p,q)(i,j,t), t=1, 2, . . . , T at i^(th)row, j^(th) column, and judging: if Re_(i,j)<DD, then g=g+1, and storingthe TTR S^(p,q)(i,j,t), t=1, 2, . . . , T in set X(g), otherwisei=i+CL^(p), and continuing to calculate the correlation Re_(i,j) betweenset X(g) and the TTR S^(p,q)(i,j,t), t=1, 2, . . . , T at i^(th) row,j^(th) column and judge, where if i>M^(p,q), then i=i−M^(p,q),j=j+CL^(q), if j>N^(p,q), then terminating the calculation and judgment,each set X(g) is a selected TTR, M^(p,q), N^(p,q) are respectively thenumber of rows and the number of columns of data block S^(p,q); puttingselected TTRs of all data blocks together to obtain the G transientthermal responses.
 3. The method for separating out a defect image froma thermogram sequence based on weighted naive Bayesian classifier anddynamic multi-objective optimization of claim 1, wherein the initial TTRpopulation corresponding to the approximate solution for multi-objectiveoptimization is chosen according to the two TTR populations respectivelycorresponding to the two approximate solutions of previous two defectimage separations by the following steps: Step A: randomly selectingN_(E) feature vectors from TTR population set _(i′) ⁻¹PS to form a TTRset _(i′) ⁻¹PS′, which is denoted by _(i′) ⁻¹PS′=(_(i′) ⁻¹X′¹, _(i′)⁻¹X′², . . . , _(i′) ⁻¹X′^(N) ^(E) ), randomly selecting N_(E) featurevectors from TTR population set _(i′) ⁻²PS to form a TTR set _(i′)⁻²PS′, where −1 represents the last defect image separation, −2represents the second-to-last defect image separation, the TTRpopulation set _(i′) ⁻¹PS corresponds to the approximate solutions ofcategory i′ of the last defect image separation, the TTR population set_(i′) ⁻²PS corresponds to the approximate solutions of category i′ ofthe second-to-last defect image separation; then marking the featurevector in TTR population set _(i′) ⁻²PS′ which is closest to the n^(th)feature vector in TTR population set _(i′) ⁻¹PS′ as _(i′) ⁻²X′^(n′),where TTR population set _(i′) ⁻²PS′ is denoted by _(i′) ⁻²PS′=(_(i′)⁻²X′¹, _(i′) ⁻²X′², . . . , _(i′) ⁻²X′^(N) ^(E) ); then calculating thenumber W of typical individuals in TTR set _(i′) ⁻¹PS′:W=┌W ₁+_(i′) ⁻¹δ×(W ₂ −W ₁)┐ where W₁ and W₂ are respectively the lowerlimit value and the upper limit value of W, and W₁=K+1, W₂=3K, _(i′) ⁻¹δis estimate of environment change of last defect image separation andobtained according to the following equations:${\,_{i^{\prime}}^{- 1}\delta} = \frac{\sum\limits_{n^{\prime} = 1}^{N_{E}}\sqrt{\sum\limits_{k = 1}^{K}\lbrack {{f_{k}( {{}_{i\prime}^{- 1}{}_{}^{\prime\mspace{11mu} n^{\prime}}} )} - {f_{k}( {{}_{i\prime}^{- 2}{}_{}^{\prime\mspace{11mu} n^{\prime}}} )}} \rbrack^{2}}}{N_{E} \times K}$f_(k)(_(i′) ⁻¹X′^(n′)) is a f_(k)(_(i′)X) into which feature vector_(i′) ⁻¹X′^(n′) as feature vector _(i′)X is plugged, f_(k)(_(i′)⁻²X′^(n′)) is a f_(k)(_(i′)X) into which feature vector _(i′) ⁻²X′^(n′)as feature vector _(i′)X is plugged; Step B: creating amulti-directional prediction set _(i′) ⁻¹C, which includes two parts,where the first part is the center of all feature vectors in TTRpopulation set _(i′) ⁻¹PS and can be denote by _(i′) ⁻¹XC¹:${{}_{i\prime}^{- 1}{}_{}^{}} = {\frac{1}{{}_{i\prime}^{- 1}{}_{}^{}}{\sum\limits_{n = 1}^{{}_{i\prime}^{- 1}{}_{}^{}}{{}_{i\prime}^{- 1}{}_{}^{}}}}$_(i′) ⁻¹X^(n) is the n^(th) feature vector in TTR population set _(i′)⁻¹PS, _(i′) ⁻¹N_(PS) is the number of feature vectors in TTR populationset _(i′) ⁻¹PS; the second part is K extreme solutions of Pareto optimalfront, and can be denote by:_(i′) ⁻¹ XC ², . . . ,_(i′) ⁻¹ XC ^(N) ^(C) N_(C) is the number offeature vectors in multi-directional prediction set _(i′) ⁻¹C,N_(C)=K+1; Step C: calculating the Euclidean distance _(i′)⁻¹D^(nw)=∥_(i′) ⁻¹X^(n)−_(i′) ⁻¹XC^(w)∥₂ of the n^(th) feature vector_(i′) ⁻¹X^(n), _(i′) ⁻¹X^(n), n=1, 2, . . . , _(i′) ⁻¹N_(PS) from eachfeature vector _(i′) ⁻¹XC^(w), w=1, 2, . . . , N_(C), and putting then^(th) feature vector _(i′) ⁻¹X^(n) into a cluster set which iscorresponding to the feature vector having minimal distance inmulti-directional prediction set _(i′) ⁻¹C, thus TTR population set_(i′) ⁻¹PS is clustered into N_(C) cluster sets which is denoted by_(i′) ⁻¹Cluster[w], w=1, 2, . . . , N_(C); Step D: If N_(C)=W,outputting multi-directional prediction set _(i′) ⁻¹C and the N_(C)cluster sets; otherwise adding a feature vector _(i′) ⁻¹XC^(N) ^(C) ⁺¹to multi-directional prediction set _(i′) ⁻¹C, then updating N_(C) withN_(C)=N_(C)+1 and returning to Step C, where feature vector _(i′)⁻¹XC^(N) ^(ps) ⁺¹ is obtained through the following equation:${{}_{i\prime}^{- 1}{}_{}^{N_{ps} + 1}} = {\arg\limits_{\,_{i^{\prime}}^{- 1}X}\;{\max\limits_{w}{\max\limits_{l}\;{{{{}_{i\prime}^{- 1}{}_{}^{wl}} - {{}_{i\prime}^{- 1}{}_{}^{}}}}}}}$_(i′) ⁻¹X^(w) ^(l) is the l^(th) feature vector of _(i′) ⁻¹Cluster[w],feature vector _(i′) ⁻¹XC^(N) ^(C) ⁺¹ is a feature vector selected fromthe N_(C) cluster sets which distance from its cluster center ismaximal; Step E: calculating a prediction direction Δ_(i′) ⁻¹C={Δ_(i′)⁻¹c¹, Δ_(i′) ⁻¹c², . . . , Δ_(i′) ⁻¹c^(W)}:Δ_(i′) ⁻¹ c ^(w)=_(i′) ⁻¹ XC ^(w)−_(i′) ⁻² XC ^(w′) ,w=1,2, . . . ,Wwhere _(i′) ⁻¹XC^(w′) is a feature vector in multi-directionalprediction set _(i′) ⁻²C of the second-to-last defect image separationwhich is closest to feature vector _(i′) ⁻¹XC^(w); Step F: initializingthe size of the initial TTR population corresponding to the approximatesolution to N_(p), where N_(p) is greater than N_(E); then creatingN_(E) feature vectors, where the n′^(th) feature vector of the N_(E)feature vectors is:_(i′) X ^(n′)(0)=_(i′) ⁻¹ X′ ^(n′)+Δ_(i′) ⁻¹ c ^(w) ^(n′) +_(i′) ⁻¹ε^(w)^(n′) ,n′=1,2, . . . ,N _(E) 0 represents initial value of iteration ofthe dynamic multi-objective optimization, w_(n′) is the serial number ofthe cluster set to which feature vector _(i′) ⁻¹X′^(n′) belongs, Δ_(i′)⁻¹c^(w) ^(n′) is the w_(n′) ^(th) element in the prediction directionΔ_(i′) ⁻¹C, _(i′) ⁻¹ε^(w) ^(n′) is a random number which obeys a normaldistribution, the mean of the normal distribution is 0, the variance ofthe normal distribution is:${\,_{i^{\prime}}^{- 1}\sigma} = {\frac{1}{W}{\sum\limits_{w = 1}^{W}{{\Delta{{}_{i\prime}^{- 1}{}_{}^{}}}}}}$randomly creating N_(P)−N_(E) feature vectors; combining the N_(E)feature vectors and the N_(P)−N_(E) feature vectors to form the initialTTR population corresponding to the approximate solution formulti-objective optimization.